Multiple choice

A man is five times as old as his son and the sum of the squares of their ages is $2106$. Find their ages.

  1. $9$ years & $45$ years
  2. $10$ yrs & $50$ years
  3. $12$ years & $48$ years
  4. $16$ years & $45$ years
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A Correct answer
Explanation

Let son's age be x, father's age be 5x. x^2 + (5x)^2 = 2106 => x^2 + 25x^2 = 2106 => 26x^2 = 2106 => x^2 = 81 => x = 9. Son is 9, father is 45.

AI explanation

Let the son's age be x years, which makes the man's age 5x years. According to the problem, the sum of the squares of their ages is x squared plus the quantity 5x squared equals 2106. This gives the equation 26 times x squared equals 2106, so x squared equals 81. Taking the positive square root gives x = 9, making their ages 9 years and 45 years respectively.

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